scholarly journals A boundary value problem for fourth-order elastic beam equations

2008 ◽  
Vol 343 (2) ◽  
pp. 1166-1176 ◽  
Author(s):  
Gabriele Bonanno ◽  
Beatrice Di Bella
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Elastic Beam ◽  
Beam Equations ◽  
Elastic Beam Equations

scholarly journals Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu
Keyword(s):  
Iterative Method ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Kirchhoff Type ◽  
Newton Iterative Method ◽  
Beam Equations ◽  
Critical Point Theorems ◽  
Elastic Beam Equations

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

scholarly journals Non-trivial solutions for nonlinear fourth-order elastic beam equations

2011 ◽  
Vol 62 (4) ◽  
pp. 1862-1869 ◽  
Author(s):  
Gabriele Bonanno ◽  
Beatrice Di Bella ◽  
Donal O’Regan
Keyword(s):  
Fourth Order ◽  
Elastic Beam ◽  
Beam Equations ◽  
Elastic Beam Equations

scholarly journals Solvability of a fourth order boundary value problem with periodic boundary conditions

1988 ◽  
Vol 11 (2) ◽  
pp. 275-284
Author(s):  
Chaitan P. Gupta
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Elastic Beam ◽  
Periodic Boundary Conditions ◽  
Uniqueness Of Solutions

Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary conditions.

scholarly journals On a Fourth-Order Boundary Value Problem at Resonance

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Man Xu ◽  
Ruyun Ma
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Elastic Beam ◽  
First Eigenvalue ◽  
At Resonance ◽  
Problem At Resonance ◽  
Spectrum Structure

We investigate the spectrum structure of the eigenvalue problem u4x=λux,  x∈0,1;  u0=u1=u′0=u′1=0. As for the application of the spectrum structure, we show the existence of solutions of the fourth-order boundary value problem at resonance -u4x+λ1ux+gx,ux=hx,  x∈0,1;  u0=u1=u′0=u′1=0, which models a statically elastic beam with both end-points being cantilevered or fixed, where λ1 is the first eigenvalue of the corresponding eigenvalue problem and nonlinearity g may be unbounded.

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